Properties

Label 5.26
Level 5
Weight 26
Dimension 21
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 52
Trace bound 1

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Defining parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 26 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(52\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{26}(\Gamma_1(5))\).

Total New Old
Modular forms 27 23 4
Cusp forms 23 21 2
Eisenstein series 4 2 2

Trace form

\( 21 q - 4002 q^{2} - 172396 q^{3} + 16772604 q^{4} + 793683685 q^{5} + 12322944112 q^{6} + 6543128808 q^{7} - 101081972280 q^{8} - 1582903387079 q^{9} + O(q^{10}) \) \( 21 q - 4002 q^{2} - 172396 q^{3} + 16772604 q^{4} + 793683685 q^{5} + 12322944112 q^{6} + 6543128808 q^{7} - 101081972280 q^{8} - 1582903387079 q^{9} + 3165827140710 q^{10} - 28877086066308 q^{11} - 68422875582512 q^{12} + 220275163302414 q^{13} - 1226233013920392 q^{14} + 790938061497620 q^{15} + 2439776746591536 q^{16} + 2841751737326178 q^{17} + 114435516345254 q^{18} + 14037065165645700 q^{19} - 45740712208111220 q^{20} + 13529319667084032 q^{21} - 24264570707350104 q^{22} + 324730477826668824 q^{23} - 1250704138692513600 q^{24} + 1419801381445966725 q^{25} - 1353210555038154348 q^{26} - 616576469248728280 q^{27} + 7460551168186390176 q^{28} - 6010709312528680650 q^{29} + 11142996804253937920 q^{30} - 11241796156071223008 q^{31} - 17481045614240873952 q^{32} + 21495795663454819408 q^{33} - 63830509289807974692 q^{34} + 63452805294951080360 q^{35} - 2552759174209817764 q^{36} + 9156020287154409318 q^{37} + 60516990815238896280 q^{38} + 58043041771740771992 q^{39} - 269511934953092923800 q^{40} + 413443038130194670242 q^{41} + 197044147055009475936 q^{42} - 1321060245929686734756 q^{43} + 2082884792406599561808 q^{44} - 2198879184684185818055 q^{45} - 1495485905003304882408 q^{46} + 2140441407206432771088 q^{47} + 4388391998086191424 q^{48} - 1494106826159251862571 q^{49} + 4374940462801066066350 q^{50} + 4189363435545032216872 q^{51} - 5358740220726552489192 q^{52} + 5582189630338765603254 q^{53} - 4893084786761986968800 q^{54} - 216430936450509169380 q^{55} - 18596802447900878269920 q^{56} + 6463841607189211455440 q^{57} + 19528677380655136236420 q^{58} - 50741052220023733715700 q^{59} + 42026906481612094664560 q^{60} - 5438402415917345050458 q^{61} - 3387185265634263698304 q^{62} + 34818662529560120817384 q^{63} + 18369606923249935936704 q^{64} - 23464502457272716910530 q^{65} + 6954375890293241009024 q^{66} + 109602276017722838891028 q^{67} - 269493353307885380540184 q^{68} + 447907587179800790690592 q^{69} - 649633568473811878161240 q^{70} + 210941655788439155610792 q^{71} + 651674850937592404267560 q^{72} - 578107228546908018325926 q^{73} - 877816668049104816589692 q^{74} - 266725603091691226420300 q^{75} + 1371715841872415755629360 q^{76} - 501697267892420228433984 q^{77} + 822483197934526611655888 q^{78} - 533613610512044940870000 q^{79} + 1934609898980050340802160 q^{80} + 545142523246056827752141 q^{81} + 1043883358198078825109196 q^{82} + 1876801646020830546135684 q^{83} - 12051525902524259815000992 q^{84} - 588892372579193591248590 q^{85} + 4134804128142689596327872 q^{86} + 5808903586894731691339160 q^{87} - 4216063541689362176038560 q^{88} - 2192776454621002905409950 q^{89} - 9866078419131404687544130 q^{90} + 19091558339488828897549872 q^{91} + 13190242110052756103759328 q^{92} - 5779813589219968851924192 q^{93} - 27379684943189219059270392 q^{94} - 18921134823614420054472700 q^{95} + 59921726409999579279571712 q^{96} + 37152087992100438181379538 q^{97} - 46079972861881665096048114 q^{98} - 52156868102585990025471508 q^{99} + O(q^{100}) \)

Decomposition of \(S_{26}^{\mathrm{new}}(\Gamma_1(5))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
5.26.a \(\chi_{5}(1, \cdot)\) 5.26.a.a 4 1
5.26.a.b 5
5.26.b \(\chi_{5}(4, \cdot)\) 5.26.b.a 12 1

Decomposition of \(S_{26}^{\mathrm{old}}(\Gamma_1(5))\) into lower level spaces

\( S_{26}^{\mathrm{old}}(\Gamma_1(5)) \cong \) \(S_{26}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)